It has been known in the past to arrange a catalyst able to store oxygen in an exhaust passage of an internal combustion engine and remove unburned gas (HC, CO, etc.) and NOX in the exhaust gas at the catalyst. The higher the oxygen storage ability of the catalyst, the greater the amount of oxygen which can be stored in the catalyst and the better the exhaust purification performance of the catalyst.
To maintain the oxygen storage ability of the catalyst, the oxygen storage amount of the catalyst preferably is made to fluctuate so that the oxygen storage amount of the catalyst is not maintained constant. In the internal combustion engine described in PTL 1, to make the oxygen storage amount of the catalyst fluctuate, the target air-fuel ratio of the exhaust gas flowing into the catalyst is alternately switched between a lean air-fuel ratio leaner than a stoichiometric air-fuel ratio and a rich air-fuel ratio richer than the stoichiometric air-fuel ratio.
Specifically, in the internal combustion engine described in PTL 1, when the air-fuel ratio detected by the downstream side air-fuel ratio sensor becomes a rich judged air-fuel ratio richer than the stoichiometric air-fuel ratio or becomes less, the target air-fuel ratio is set to the lean air-fuel ratio, while when the air-fuel ratio detected by the downstream side air-fuel ratio sensor becomes a lean judged air-fuel ratio leaner than the stoichiometric air-fuel ratio or becomes more, the target air-fuel ratio is set to the rich air-fuel ratio. In the internal combustion engine described in PTL 2, when the air-fuel ratio detected by the downstream side air-fuel ratio sensor becomes a rich judged air-fuel ratio richer than the stoichiometric air-fuel ratio or becomes less, the target air-fuel ratio is set to the lean air-fuel ratio, while when the estimated value of the oxygen storage amount of the catalyst becomes a switching reference storage amount or more, the target air-fuel ratio is set to the rich air-fuel ratio.